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JEE Main 2023 · Physics · Thermodynamics and Kinetic Theory of Gases · easy

A rigid-molecule gas mixture contains 2 mol of helium and 3 mol of oxygen.

Single correct option

A rigid-molecule gas mixture contains 22 mol of helium and 33 mol of oxygen. The ratio Cp/CvC_p/C_v of the mixture is
  1. A. 32\dfrac{3}{2}
  2. B. 2921\dfrac{29}{21}
  3. C. 75\dfrac{7}{5}
  4. D. 3121\dfrac{31}{21}
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Answer: (D) 3121\dfrac{31}{21}

Helium: Cv=32RC_v=\tfrac32R; oxygen (diatomic, rigid): Cv=52RC_v=\tfrac52R. For the mixture Cv=2(1.5R)+3(2.5R)5=2.1R=2110RC_v=\dfrac{2(1.5R)+3(2.5R)}{5}=2.1R=\dfrac{21}{10}R and Cp=Cv+R=3110RC_p=C_v+R=\dfrac{31}{10}R. So γ=3121\gamma=\dfrac{31}{21}. Averaging the individual γ\gamma values (5/35/3 and 7/57/5) is not valid.
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